LMFDB - Embedded newform 980.2.o.b.411.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(31,980)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("980.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			411.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.411
Dual form			980.2.o.b.31.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-1.00000 - 1.00000i) q^{10} +(0.232051 - 0.133975i) q^{11} -3.46410i q^{12} -0.464102i q^{13} -1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-5.59808 + 3.23205i) q^{17} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} +(-0.366025 + 0.0980762i) q^{22} +(-1.26795 - 0.732051i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.169873 + 0.633975i) q^{26} -5.19615 q^{27} +7.92820 q^{29} +(-0.633975 + 2.36603i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-0.401924 - 0.232051i) q^{33} +(8.83013 - 2.36603i) q^{34} +(4.73205 - 8.19615i) q^{37} +(-6.00000 + 6.00000i) q^{38} +(-0.696152 + 0.401924i) q^{39} +(-0.732051 - 2.73205i) q^{40} -3.46410i q^{41} +2.00000i q^{43} +0.535898 q^{44} +(1.46410 + 1.46410i) q^{46} +(0.866025 - 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-0.366025 - 1.36603i) q^{50} +(9.69615 + 5.59808i) q^{51} +(0.464102 - 0.803848i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(7.09808 + 1.90192i) q^{54} +0.267949 q^{55} -10.3923 q^{57} +(-10.8301 - 2.90192i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(1.73205 - 3.00000i) q^{60} +(-8.19615 - 4.73205i) q^{61} +(2.19615 + 8.19615i) q^{62} +8.00000i q^{64} +(0.232051 - 0.401924i) q^{65} +(0.464102 + 0.464102i) q^{66} +(-3.00000 + 1.73205i) q^{67} -12.9282 q^{68} +2.53590i q^{69} +7.46410i q^{71} +(11.1962 - 6.46410i) q^{73} +(-9.46410 + 9.46410i) q^{74} +(0.866025 - 1.50000i) q^{75} +(10.3923 - 6.00000i) q^{76} +(1.09808 - 0.294229i) q^{78} +(-12.6962 - 7.33013i) q^{79} +4.00000i q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.26795 + 4.73205i) q^{82} -15.4641 q^{83} -6.46410 q^{85} +(0.732051 - 2.73205i) q^{86} +(-6.86603 - 11.8923i) q^{87} +(-0.732051 - 0.196152i) q^{88} +(-2.19615 - 1.26795i) q^{89} +(-1.46410 - 2.53590i) q^{92} +(-5.19615 + 9.00000i) q^{93} +(-1.73205 + 1.73205i) q^{94} +(5.19615 - 3.00000i) q^{95} +(-6.92820 + 6.92820i) q^{96} -13.3923i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} - 4 q^{10} - 6 q^{11} + 8 q^{16} - 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} - 12 q^{23} - 12 q^{24} + 2 q^{25} - 18 q^{26} + 4 q^{29} - 6 q^{30} - 12 q^{31} + 8 q^{32} - 12 q^{33} + 18 q^{34} + 12 q^{37} - 24 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{44} - 8 q^{46} + 2 q^{50} + 18 q^{51} - 12 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 26 q^{58} - 12 q^{61} - 12 q^{62} - 6 q^{65} - 12 q^{66} - 12 q^{67} - 24 q^{68} + 24 q^{73} - 24 q^{74} - 6 q^{78} - 30 q^{79} + 18 q^{81} - 12 q^{82} - 48 q^{83} - 12 q^{85} - 4 q^{86} - 24 q^{87} + 4 q^{88} + 12 q^{89} + 8 q^{92}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 - 4 * q^10 - 6 * q^11 + 8 * q^16 - 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 - 12 * q^23 - 12 * q^24 + 2 * q^25 - 18 * q^26 + 4 * q^29 - 6 * q^30 - 12 * q^31 + 8 * q^32 - 12 * q^33 + 18 * q^34 + 12 * q^37 - 24 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^44 - 8 * q^46 + 2 * q^50 + 18 * q^51 - 12 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 26 * q^58 - 12 * q^61 - 12 * q^62 - 6 * q^65 - 12 * q^66 - 12 * q^67 - 24 * q^68 + 24 * q^73 - 24 * q^74 - 6 * q^78 - 30 * q^79 + 18 * q^81 - 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 - 24 * q^87 + 4 * q^88 + 12 * q^89 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	−1.00000			$\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	0.633975	+	2.36603i	0.258819	+	0.965926i
$7$		0			0
$7$		0			0
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	−1.00000	−	1.00000i	−0.316228	−	0.316228i
$11$	0.232051	−	0.133975i	0.0699660	−	0.0403949i	−0.464609	−	0.885516i	$-0.653805\pi$
$11$	0.232051	−	0.133975i	0.0699660	−	0.0403949i	0.534575	+	0.845121i	$0.320472\pi$
$12$		−	3.46410i		−	1.00000i
$13$		−	0.464102i		−	0.128719i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$		−	0.464102i		−	0.128719i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		−	1.73205i		−	0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−5.59808	+	3.23205i	−1.35773	+	0.783887i	−0.989318	−	0.145774i	$-0.953433\pi$
$17$	−5.59808	+	3.23205i	−1.35773	+	0.783887i	−0.368415	+	0.929661i	$0.620099\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	−0.366025	+	0.0980762i	−0.0780369	+	0.0209099i
$23$	−1.26795	−	0.732051i	−0.264386	−	0.152643i	0.361948	−	0.932198i	$-0.382112\pi$
$23$	−1.26795	−	0.732051i	−0.264386	−	0.152643i	−0.626334	+	0.779555i	$0.715445\pi$
$24$	−1.26795	+	4.73205i	−0.258819	+	0.965926i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.169873	+	0.633975i	−0.0333148	+	0.124333i
$27$	−5.19615			−1.00000
$28$		0			0
$29$	7.92820			1.47223			0.736115	−	0.676856i	$-0.236658\pi$
$29$	7.92820			1.47223			0.736115	+	0.676856i	$0.236658\pi$
$30$	−0.633975	+	2.36603i	−0.115747	+	0.431975i
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$	−0.401924	−	0.232051i	−0.0699660	−	0.0403949i
$34$	8.83013	−	2.36603i	1.51435	−	0.405770i
$35$		0			0
$36$		0			0
$37$	4.73205	−	8.19615i	0.777944	−	1.34744i	−0.155180	−	0.987886i	$-0.549596\pi$
$37$	4.73205	−	8.19615i	0.777944	−	1.34744i	0.933125	−	0.359553i	$-0.117071\pi$
$38$	−6.00000	+	6.00000i	−0.973329	+	0.973329i
$39$	−0.696152	+	0.401924i	−0.111474	+	0.0643593i
$40$	−0.732051	−	2.73205i	−0.115747	−	0.431975i
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	0.535898			0.0807897
$45$		0			0
$46$	1.46410	+	1.46410i	0.215870	+	0.215870i
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	−0.795926	−	0.605393i	$-0.793016\pi$
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	0.922249	+	0.386596i	$0.126349\pi$
$48$	3.46410	−	6.00000i	0.500000	−	0.866025i
$49$		0			0
$50$	−0.366025	−	1.36603i	−0.0517638	−	0.193185i
$51$	9.69615	+	5.59808i	1.35773	+	0.783887i
$52$	0.464102	−	0.803848i	0.0643593	−	0.111474i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$	7.09808	+	1.90192i	0.965926	+	0.258819i
$55$	0.267949			0.0361303
$56$		0			0
$57$	−10.3923			−1.37649
$58$	−10.8301	−	2.90192i	−1.42207	−	0.381041i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$	1.73205	−	3.00000i	0.223607	−	0.387298i
$61$	−8.19615	−	4.73205i	−1.04941	−	0.605877i	−0.126926	−	0.991912i	$-0.540511\pi$
$61$	−8.19615	−	4.73205i	−1.04941	−	0.605877i	−0.922484	+	0.386035i	$0.873844\pi$
$62$	2.19615	+	8.19615i	0.278912	+	1.04091i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	0.232051	−	0.401924i	0.0287824	−	0.0498525i
$66$	0.464102	+	0.464102i	0.0571270	+	0.0571270i
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	0.305424	+	0.952217i	$0.401202\pi$
$68$	−12.9282			−1.56777
$69$			2.53590i			0.305286i
$70$		0			0
$71$			7.46410i			0.885826i	0.896565	+	0.442913i	$0.146055\pi$
$71$			7.46410i			0.885826i	−0.896565	+	0.442913i	$0.853945\pi$
$72$		0			0
$73$	11.1962	−	6.46410i	1.31041	−	0.756566i	0.328247	−	0.944592i	$-0.393542\pi$
$73$	11.1962	−	6.46410i	1.31041	−	0.756566i	0.982164	+	0.188026i	$0.0602090\pi$
$74$	−9.46410	+	9.46410i	−1.10018	+	1.10018i
$75$	0.866025	−	1.50000i	0.100000	−	0.173205i
$76$	10.3923	−	6.00000i	1.19208	−	0.688247i
$77$		0			0
$78$	1.09808	−	0.294229i	0.124333	−	0.0333148i
$79$	−12.6962	−	7.33013i	−1.42843	−	0.824704i	−0.431432	−	0.902146i	$-0.641991\pi$
$79$	−12.6962	−	7.33013i	−1.42843	−	0.824704i	−0.996997	+	0.0774418i	$0.975325\pi$
$80$			4.00000i			0.447214i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−1.26795	+	4.73205i	−0.140022	+	0.522568i
$83$	−15.4641			−1.69741			−0.848703	−	0.528870i	$-0.822616\pi$
$83$	−15.4641			−1.69741			−0.848703	+	0.528870i	$0.822616\pi$
$84$		0			0
$85$	−6.46410			−0.701130
$86$	0.732051	−	2.73205i	0.0789391	−	0.294605i
$87$	−6.86603	−	11.8923i	−0.736115	−	1.27499i
$88$	−0.732051	−	0.196152i	−0.0780369	−	0.0209099i
$89$	−2.19615	−	1.26795i	−0.232792	−	0.134402i	0.379068	−	0.925369i	$-0.376245\pi$
$89$	−2.19615	−	1.26795i	−0.232792	−	0.134402i	−0.611859	+	0.790967i	$0.709578\pi$
$90$		0			0
$91$		0			0
$92$	−1.46410	−	2.53590i	−0.152643	−	0.264386i
$93$	−5.19615	+	9.00000i	−0.538816	+	0.933257i
$94$	−1.73205	+	1.73205i	−0.178647	+	0.178647i
$95$	5.19615	−	3.00000i	0.533114	−	0.307794i
$96$	−6.92820	+	6.92820i	−0.707107	+	0.707107i
$97$		−	13.3923i		−	1.35978i	−0.733313	−	0.679891i	$-0.762027\pi$
$97$		−	13.3923i		−	1.35978i	0.733313	−	0.679891i	$-0.237973\pi$
$98$		0			0
$99$		0			0
$100$			2.00000i			0.200000i
$101$	−13.3923	+	7.73205i	−1.33258	+	0.769368i	−0.985695	−	0.168538i	$-0.946095\pi$
$101$	−13.3923	+	7.73205i	−1.33258	+	0.769368i	−0.346889	+	0.937906i	$0.612762\pi$
$102$	−11.1962	−	11.1962i	−1.10858	−	1.10858i
$103$	−3.40192	+	5.89230i	−0.335202	+	0.580586i	−0.983524	−	0.180780i	$-0.942138\pi$
$103$	−3.40192	+	5.89230i	−0.335202	+	0.580586i	0.648322	+	0.761366i	$0.275471\pi$
$104$	−0.928203	+	0.928203i	−0.0910178	+	0.0910178i
$105$		0			0
$106$	0.732051	+	2.73205i	0.0711031	+	0.265360i
$107$	2.07180	+	1.19615i	0.200288	+	0.115636i	0.596790	−	0.802398i	$-0.296443\pi$
$107$	2.07180	+	1.19615i	0.200288	+	0.115636i	−0.396502	+	0.918034i	$0.629776\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	−1.03590	−	1.79423i	−0.0992211	−	0.171856i	0.812141	−	0.583461i	$-0.198302\pi$
$109$	−1.03590	−	1.79423i	−0.0992211	−	0.171856i	−0.911362	+	0.411605i	$0.864968\pi$
$110$	−0.366025	−	0.0980762i	−0.0348992	−	0.00935120i
$111$	−16.3923			−1.55589
$112$		0			0
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$	14.1962	+	3.80385i	1.32959	+	0.356263i
$115$	−0.732051	−	1.26795i	−0.0682641	−	0.118237i
$116$	13.7321	+	7.92820i	1.27499	+	0.736115i
$117$		0			0
$118$	1.26795	+	4.73205i	0.116724	+	0.435621i
$119$		0			0
$120$	−3.46410	+	3.46410i	−0.316228	+	0.316228i
$121$	−5.46410	+	9.46410i	−0.496737	+	0.860373i
$122$	9.46410	+	9.46410i	0.856840	+	0.856840i
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$		−	12.0000i		−	1.07763i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	15.4641i		−	1.37222i	−0.727499	−	0.686109i	$-0.759317\pi$
$127$		−	15.4641i		−	1.37222i	0.727499	−	0.686109i	$-0.240683\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$	3.00000	−	1.73205i	0.264135	−	0.152499i
$130$	−0.464102	+	0.464102i	−0.0407044	+	0.0407044i
$131$	1.26795	−	2.19615i	0.110781	−	0.191879i	−0.805304	−	0.592862i	$-0.797998\pi$
$131$	1.26795	−	2.19615i	0.110781	−	0.191879i	0.916085	+	0.400983i	$0.131331\pi$
$132$	−0.464102	−	0.803848i	−0.0403949	−	0.0699660i
$133$		0			0
$134$	4.73205	−	1.26795i	0.408787	−	0.109534i
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	17.6603	+	4.73205i	1.51435	+	0.405770i
$137$	−10.1962	−	17.6603i	−0.871116	−	1.50882i	−0.860843	−	0.508870i	$-0.830063\pi$
$137$	−10.1962	−	17.6603i	−0.871116	−	1.50882i	−0.0102728	−	0.999947i	$-0.503270\pi$
$138$	0.928203	−	3.46410i	0.0790139	−	0.294884i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	2.73205	−	10.1962i	0.229269	−	0.855642i
$143$	−0.0621778	−	0.107695i	−0.00519957	−	0.00900592i
$144$		0			0
$145$	6.86603	+	3.96410i	0.570192	+	0.329201i
$146$	−17.6603	+	4.73205i	−1.46157	+	0.391627i
$147$		0			0
$148$	16.3923	−	9.46410i	1.34744	−	0.777944i
$149$	−1.53590	+	2.66025i	−0.125826	+	0.217937i	−0.922055	−	0.387058i	$-0.873491\pi$
$149$	−1.53590	+	2.66025i	−0.125826	+	0.217937i	0.796230	+	0.604994i	$0.206825\pi$
$150$	−1.73205	+	1.73205i	−0.141421	+	0.141421i
$151$	13.1603	−	7.59808i	1.07097	−	0.618323i	0.142521	−	0.989792i	$-0.454479\pi$
$151$	13.1603	−	7.59808i	1.07097	−	0.618323i	0.928445	+	0.371469i	$0.121146\pi$
$152$	−16.3923	+	4.39230i	−1.32959	+	0.356263i
$153$		0			0
$154$		0			0
$155$		−	6.00000i		−	0.481932i
$156$	−1.60770			−0.128719
$157$	6.80385	−	3.92820i	0.543006	−	0.313505i	−0.203290	−	0.979119i	$-0.565163\pi$
$157$	6.80385	−	3.92820i	0.543006	−	0.313505i	0.746296	+	0.665614i	$0.231830\pi$
$158$	14.6603	+	14.6603i	1.16631	+	1.16631i
$159$	−1.73205	+	3.00000i	−0.137361	+	0.237915i
$160$	1.46410	−	5.46410i	0.115747	−	0.431975i
$161$		0			0
$162$	−3.29423	−	12.2942i	−0.258819	−	0.965926i
$163$	18.0000	+	10.3923i	1.40987	+	0.813988i	0.995375	−	0.0960641i	$-0.0306254\pi$
$163$	18.0000	+	10.3923i	1.40987	+	0.813988i	0.414494	+	0.910052i	$0.363959\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$	−0.232051	−	0.401924i	−0.0180651	−	0.0312897i
$166$	21.1244	+	5.66025i	1.63957	+	0.439321i
$167$	5.19615			0.402090			0.201045	−	0.979582i	$-0.435566\pi$
$167$	5.19615			0.402090			0.201045	+	0.979582i	$0.435566\pi$
$168$		0			0
$169$	12.7846			0.983432
$170$	8.83013	+	2.36603i	0.677240	+	0.181466i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	12.4019	+	7.16025i	0.942901	+	0.544384i	0.890868	−	0.454261i	$-0.150097\pi$
$173$	12.4019	+	7.16025i	0.942901	+	0.544384i	0.0520323	+	0.998645i	$0.483430\pi$
$174$	5.02628	+	18.7583i	0.381041	+	1.42207i
$175$		0			0
$176$	0.928203	+	0.535898i	0.0699660	+	0.0403949i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	2.53590	+	2.53590i	0.190074	+	0.190074i
$179$	−5.53590	+	3.19615i	−0.413772	+	0.238892i	−0.692409	−	0.721505i	$-0.743451\pi$
$179$	−5.53590	+	3.19615i	−0.413772	+	0.238892i	0.278637	+	0.960397i	$0.410117\pi$
$180$		0			0
$181$		−	0.928203i		−	0.0689928i	−0.999405	−	0.0344964i	$-0.989017\pi$
$181$		−	0.928203i		−	0.0689928i	0.999405	−	0.0344964i	$-0.0109827\pi$
$182$		0			0
$183$			16.3923i			1.21175i
$184$	1.07180	+	4.00000i	0.0790139	+	0.294884i
$185$	8.19615	−	4.73205i	0.602593	−	0.347907i
$186$	10.3923	−	10.3923i	0.762001	−	0.762001i
$187$	−0.866025	+	1.50000i	−0.0633300	+	0.109691i
$188$	3.00000	−	1.73205i	0.218797	−	0.126323i
$189$		0			0
$190$	−8.19615	+	2.19615i	−0.594611	+	0.159326i
$191$	−6.23205	−	3.59808i	−0.450935	−	0.260348i	0.257290	−	0.966334i	$-0.417171\pi$
$191$	−6.23205	−	3.59808i	−0.450935	−	0.260348i	−0.708225	+	0.705987i	$0.750504\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	4.73205	+	8.19615i	0.340620	+	0.589972i	0.984548	−	0.175114i	$-0.0560296\pi$
$193$	4.73205	+	8.19615i	0.340620	+	0.589972i	−0.643928	+	0.765086i	$0.722696\pi$
$194$	−4.90192	+	18.2942i	−0.351938	+	1.31345i
$195$	−0.803848			−0.0575647
$196$		0			0
$197$	−13.3205			−0.949047			−0.474523	−	0.880243i	$-0.657380\pi$
$197$	−13.3205			−0.949047			−0.474523	+	0.880243i	$0.657380\pi$
$198$		0			0
$199$	1.73205	+	3.00000i	0.122782	+	0.212664i	0.920864	−	0.389885i	$-0.127485\pi$
$199$	1.73205	+	3.00000i	0.122782	+	0.212664i	−0.798082	+	0.602549i	$0.794152\pi$
$200$	0.732051	−	2.73205i	0.0517638	−	0.193185i
$201$	5.19615	+	3.00000i	0.366508	+	0.211604i
$202$	21.1244	−	5.66025i	1.48630	−	0.398254i
$203$		0			0
$204$	11.1962	+	19.3923i	0.783887	+	1.35773i
$205$	1.73205	−	3.00000i	0.120972	−	0.209529i
$206$	6.80385	−	6.80385i	0.474047	−	0.474047i
$207$		0			0
$208$	1.60770	−	0.928203i	0.111474	−	0.0643593i
$209$		−	1.60770i		−	0.111207i
$210$		0			0
$211$			3.19615i			0.220032i	0.993930	+	0.110016i	$0.0350902\pi$
$211$			3.19615i			0.220032i	−0.993930	+	0.110016i	$0.964910\pi$
$212$		−	4.00000i		−	0.274721i
$213$	11.1962	−	6.46410i	0.767148	−	0.442913i
$214$	−2.39230	−	2.39230i	−0.163535	−	0.163535i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$		0			0
$218$	0.758330	+	2.83013i	0.0513606	+	0.191680i
$219$	−19.3923	−	11.1962i	−1.31041	−	0.756566i
$220$	0.464102	+	0.267949i	0.0312897	+	0.0180651i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$	22.3923	+	6.00000i	1.50287	+	0.402694i
$223$	13.7321			0.919566			0.459783	−	0.888031i	$-0.347927\pi$
$223$	13.7321			0.919566			0.459783	+	0.888031i	$0.347927\pi$
$224$		0			0
$225$		0			0
$226$	−7.46410	−	2.00000i	−0.496505	−	0.133038i
$227$	10.3301	+	17.8923i	0.685635	+	1.18755i	0.973237	+	0.229804i	$0.0738085\pi$
$227$	10.3301	+	17.8923i	0.685635	+	1.18755i	−0.287602	+	0.957750i	$0.592858\pi$
$228$	−18.0000	−	10.3923i	−1.19208	−	0.688247i
$229$	7.39230	+	4.26795i	0.488497	+	0.282034i	0.723951	−	0.689852i	$-0.242324\pi$
$229$	7.39230	+	4.26795i	0.488497	+	0.282034i	−0.235454	+	0.971886i	$0.575658\pi$
$230$	0.535898	+	2.00000i	0.0353361	+	0.131876i
$231$		0			0
$232$	−15.8564	−	15.8564i	−1.04102	−	1.04102i
$233$	4.53590	−	7.85641i	0.297157	−	0.514690i	−0.678328	−	0.734760i	$-0.737295\pi$
$233$	4.53590	−	7.85641i	0.297157	−	0.514690i	0.975484	+	0.220069i	$0.0706283\pi$
$234$		0			0
$235$	1.50000	−	0.866025i	0.0978492	−	0.0564933i
$236$		−	6.92820i		−	0.450988i
$237$			25.3923i			1.64941i
$238$		0			0
$239$		−	23.9808i		−	1.55119i	−0.631233	−	0.775593i	$-0.717451\pi$
$239$		−	23.9808i		−	1.55119i	0.631233	−	0.775593i	$-0.282549\pi$
$240$	6.00000	−	3.46410i	0.387298	−	0.223607i
$241$	14.1962	−	8.19615i	0.914455	−	0.527961i	0.0325928	−	0.999469i	$-0.489624\pi$
$241$	14.1962	−	8.19615i	0.914455	−	0.527961i	0.881862	+	0.471508i	$0.156290\pi$
$242$	10.9282	−	10.9282i	0.702492	−	0.702492i
$243$		0			0
$244$	−9.46410	−	16.3923i	−0.605877	−	1.04941i
$245$		0			0
$246$	8.19615	−	2.19615i	0.522568	−	0.140022i
$247$	−2.41154	−	1.39230i	−0.153443	−	0.0885902i
$248$	−4.39230	+	16.3923i	−0.278912	+	1.04091i
$249$	13.3923	+	23.1962i	0.848703	+	1.47000i
$250$	0.366025	−	1.36603i	0.0231495	−	0.0863950i
$251$	25.8564			1.63204			0.816021	−	0.578022i	$-0.196175\pi$
$251$	25.8564			1.63204			0.816021	+	0.578022i	$0.196175\pi$
$252$		0			0
$253$	−0.392305			−0.0246640
$254$	−5.66025	+	21.1244i	−0.355156	+	1.32546i
$255$	5.59808	+	9.69615i	0.350565	+	0.607197i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	0.329104	−	0.944294i	$-0.393253\pi$
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	−0.653231	+	0.757159i	$0.726587\pi$
$258$	−4.73205	+	1.26795i	−0.294605	+	0.0789391i
$259$		0			0
$260$	0.803848	−	0.464102i	0.0498525	−	0.0287824i
$261$		0			0
$262$	−2.53590	+	2.53590i	−0.156668	+	0.156668i
$263$	−9.92820	+	5.73205i	−0.612199	+	0.353453i	−0.773826	−	0.633399i	$-0.781659\pi$
$263$	−9.92820	+	5.73205i	−0.612199	+	0.353453i	0.161626	+	0.986852i	$0.448326\pi$
$264$	0.339746	+	1.26795i	0.0209099	+	0.0780369i
$265$		−	2.00000i		−	0.122859i
$266$		0			0
$267$			4.39230i			0.268805i
$268$	−6.92820			−0.423207
$269$	−10.3923	+	6.00000i	−0.633630	+	0.365826i	−0.782157	−	0.623082i	$-0.785880\pi$
$269$	−10.3923	+	6.00000i	−0.633630	+	0.365826i	0.148527	+	0.988908i	$0.452547\pi$
$270$	5.19615	+	5.19615i	0.316228	+	0.316228i
$271$	4.73205	−	8.19615i	0.287452	−	0.497881i	−0.685749	−	0.727838i	$-0.740525\pi$
$271$	4.73205	−	8.19615i	0.287452	−	0.497881i	0.973201	+	0.229957i	$0.0738586\pi$
$272$	−22.3923	−	12.9282i	−1.35773	−	0.783887i
$273$		0			0
$274$	7.46410	+	27.8564i	0.450923	+	1.68287i
$275$	0.232051	+	0.133975i	0.0139932	+	0.00807897i
$276$	−2.53590	+	4.39230i	−0.152643	+	0.264386i
$277$	−8.39230	−	14.5359i	−0.504245	−	0.873377i	−0.999988	−	0.00490834i	$-0.998438\pi$
$277$	−8.39230	−	14.5359i	−0.504245	−	0.873377i	0.495743	−	0.868469i	$-0.334896\pi$
$278$	9.46410	+	2.53590i	0.567619	+	0.152093i
$279$		0			0
$280$		0			0
$281$	−7.92820			−0.472957			−0.236478	−	0.971637i	$-0.575993\pi$
$281$	−7.92820			−0.472957			−0.236478	+	0.971637i	$0.575993\pi$
$282$	4.09808	+	1.09808i	0.244037	+	0.0653895i
$283$	6.06218	+	10.5000i	0.360359	+	0.624160i	0.988020	−	0.154327i	$-0.0493208\pi$
$283$	6.06218	+	10.5000i	0.360359	+	0.624160i	−0.627661	+	0.778487i	$0.715988\pi$
$284$	−7.46410	+	12.9282i	−0.442913	+	0.767148i
$285$	−9.00000	−	5.19615i	−0.533114	−	0.307794i
$286$	0.0455173	+	0.169873i	0.00269150	+	0.0100448i
$287$		0			0
$288$		0			0
$289$	12.3923	−	21.4641i	0.728959	−	1.26259i
$290$	−7.92820	−	7.92820i	−0.465560	−	0.465560i
$291$	−20.0885	+	11.5981i	−1.17761	+	0.679891i
$292$	25.8564			1.51313
$293$			20.3205i			1.18714i	0.804784	+	0.593568i	$0.202281\pi$
$293$			20.3205i			1.18714i	−0.804784	+	0.593568i	$0.797719\pi$
$294$		0			0
$295$		−	3.46410i		−	0.201688i
$296$	−25.8564	+	6.92820i	−1.50287	+	0.402694i
$297$	−1.20577	+	0.696152i	−0.0699660	+	0.0403949i
$298$	3.07180	−	3.07180i	0.177944	−	0.177944i
$299$	−0.339746	+	0.588457i	−0.0196480	+	0.0340314i
$300$	3.00000	−	1.73205i	0.173205	−	0.100000i
$301$		0			0
$302$	−20.7583	+	5.56218i	−1.19451	+	0.320067i
$303$	23.1962	+	13.3923i	1.33258	+	0.769368i
$304$	24.0000			1.37649
$305$	−4.73205	−	8.19615i	−0.270956	−	0.469310i
$306$		0			0
$307$	−1.73205			−0.0988534			−0.0494267	−	0.998778i	$-0.515739\pi$
$307$	−1.73205			−0.0988534			−0.0494267	+	0.998778i	$0.515739\pi$
$308$		0			0
$309$	11.7846			0.670403
$310$	−2.19615	+	8.19615i	−0.124733	+	0.465510i
$311$	3.92820	+	6.80385i	0.222748	+	0.385811i	0.955641	−	0.294533i	$-0.0951640\pi$
$311$	3.92820	+	6.80385i	0.222748	+	0.385811i	−0.732893	+	0.680343i	$0.761831\pi$
$312$	2.19615	+	0.588457i	0.124333	+	0.0333148i
$313$	15.1865	+	8.76795i	0.858394	+	0.495594i	0.863474	−	0.504393i	$-0.168284\pi$
$313$	15.1865	+	8.76795i	0.858394	+	0.495594i	−0.00508040	+	0.999987i	$0.501617\pi$
$314$	−10.7321	+	2.87564i	−0.605645	+	0.162282i
$315$		0			0
$316$	−14.6603	−	25.3923i	−0.824704	−	1.42843i
$317$	1.53590	−	2.66025i	0.0862646	−	0.149415i	−0.819665	−	0.572844i	$-0.805840\pi$
$317$	1.53590	−	2.66025i	0.0862646	−	0.149415i	0.905929	+	0.423429i	$0.139174\pi$
$318$	3.46410	−	3.46410i	0.194257	−	0.194257i
$319$	1.83975	−	1.06218i	0.103006	−	0.0594705i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$		−	4.14359i		−	0.231273i
$322$		0			0
$323$			38.7846i			2.15803i
$324$			18.0000i			1.00000i
$325$	0.401924	−	0.232051i	0.0222947	−	0.0128719i
$326$	−20.7846	−	20.7846i	−1.15115	−	1.15115i
$327$	−1.79423	+	3.10770i	−0.0992211	+	0.171856i
$328$	−6.92820	+	6.92820i	−0.382546	+	0.382546i
$329$		0			0
$330$	0.169873	+	0.633975i	0.00935120	+	0.0348992i
$331$	22.8564	+	13.1962i	1.25630	+	0.725326i	0.972354	−	0.233513i	$-0.0750223\pi$
$331$	22.8564	+	13.1962i	1.25630	+	0.725326i	0.283948	+	0.958840i	$0.408356\pi$
$332$	−26.7846	−	15.4641i	−1.47000	−	0.848703i
$333$		0			0
$334$	−7.09808	−	1.90192i	−0.388389	−	0.104069i
$335$	−3.46410			−0.189264
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−17.4641	−	4.67949i	−0.949922	−	0.254531i
$339$	−4.73205	−	8.19615i	−0.257010	−	0.445154i
$340$	−11.1962	−	6.46410i	−0.607197	−	0.350565i
$341$	−1.39230	−	0.803848i	−0.0753975	−	0.0435308i
$342$		0			0
$343$		0			0
$344$	4.00000	−	4.00000i	0.215666	−	0.215666i
$345$	−1.26795	+	2.19615i	−0.0682641	+	0.118237i
$346$	−14.3205	−	14.3205i	−0.769875	−	0.769875i
$347$	29.6603	−	17.1244i	1.59225	−	0.919284i	0.599325	−	0.800506i	$-0.295436\pi$
$347$	29.6603	−	17.1244i	1.59225	−	0.919284i	0.992921	−	0.118778i	$-0.0378976\pi$
$348$		−	27.4641i		−	1.47223i
$349$		−	5.32051i		−	0.284800i	−0.989809	−	0.142400i	$-0.954518\pi$
$349$		−	5.32051i		−	0.284800i	0.989809	−	0.142400i	$-0.0454820\pi$
$350$		0			0
$351$			2.41154i			0.128719i
$352$	−1.07180	−	1.07180i	−0.0571270	−	0.0571270i
$353$	−6.40192	+	3.69615i	−0.340740	+	0.196726i	−0.660599	−	0.750739i	$-0.729698\pi$
$353$	−6.40192	+	3.69615i	−0.340740	+	0.196726i	0.319859	+	0.947465i	$0.396364\pi$
$354$	6.00000	−	6.00000i	0.318896	−	0.318896i
$355$	−3.73205	+	6.46410i	−0.198077	+	0.343079i
$356$	−2.53590	−	4.39230i	−0.134402	−	0.232792i
$357$		0			0
$358$	8.73205	−	2.33975i	0.461503	−	0.123659i
$359$	−21.9282	−	12.6603i	−1.15733	−	0.668183i	−0.206665	−	0.978412i	$-0.566261\pi$
$359$	−21.9282	−	12.6603i	−1.15733	−	0.668183i	−0.950662	+	0.310229i	$0.899594\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−0.339746	+	1.26795i	−0.0178567	+	0.0666419i
$363$	18.9282			0.993473
$364$		0			0
$365$	12.9282			0.676693
$366$	6.00000	−	22.3923i	0.313625	−	1.17046i
$367$	5.93782	+	10.2846i	0.309952	+	0.536852i	0.978352	−	0.206950i	$-0.0663537\pi$
$367$	5.93782	+	10.2846i	0.309952	+	0.536852i	−0.668400	+	0.743802i	$0.733020\pi$
$368$		−	5.85641i		−	0.305286i
$369$		0			0
$370$	−12.9282	+	3.46410i	−0.672105	+	0.180090i
$371$		0			0
$372$	−18.0000	+	10.3923i	−0.933257	+	0.538816i
$373$	1.80385	−	3.12436i	0.0933997	−	0.161773i	−0.815540	−	0.578701i	$-0.803560\pi$
$373$	1.80385	−	3.12436i	0.0933997	−	0.161773i	0.908940	+	0.416928i	$0.136893\pi$
$374$	1.73205	−	1.73205i	0.0895622	−	0.0895622i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−4.73205	+	1.26795i	−0.244037	+	0.0653895i
$377$		−	3.67949i		−	0.189503i
$378$		0			0
$379$			5.60770i			0.288048i	0.989574	+	0.144024i	$0.0460042\pi$
$379$			5.60770i			0.288048i	−0.989574	+	0.144024i	$0.953996\pi$
$380$	12.0000			0.615587
$381$	−23.1962	+	13.3923i	−1.18837	+	0.686109i
$382$	7.19615	+	7.19615i	0.368187	+	0.368187i
$383$	13.7321	−	23.7846i	0.701675	−	1.21534i	−0.266203	−	0.963917i	$-0.585769\pi$
$383$	13.7321	−	23.7846i	0.701675	−	1.21534i	0.967878	−	0.251420i	$-0.0808975\pi$
$384$	−18.9282	+	5.07180i	−0.965926	+	0.258819i
$385$		0			0
$386$	−3.46410	−	12.9282i	−0.176318	−	0.658028i
$387$		0			0
$388$	13.3923	−	23.1962i	0.679891	−	1.17761i
$389$	10.4282	+	18.0622i	0.528731	+	0.915789i	0.999439	+	0.0334996i	$0.0106653\pi$
$389$	10.4282	+	18.0622i	0.528731	+	0.915789i	−0.470708	+	0.882289i	$0.656001\pi$
$390$	1.09808	+	0.294229i	0.0556033	+	0.0148988i
$391$	9.46410			0.478620
$392$		0			0
$393$	−4.39230			−0.221562
$394$	18.1962	+	4.87564i	0.916709	+	0.245631i
$395$	−7.33013	−	12.6962i	−0.368819	−	0.638813i
$396$		0			0
$397$	−10.7942	−	6.23205i	−0.541747	−	0.312778i	0.204040	−	0.978963i	$-0.434593\pi$
$397$	−10.7942	−	6.23205i	−0.541747	−	0.312778i	−0.745787	+	0.666185i	$0.767926\pi$
$398$	−1.26795	−	4.73205i	−0.0635566	−	0.237196i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	5.03590	−	8.72243i	0.251481	−	0.435577i	−0.712453	−	0.701720i	$-0.752416\pi$
$401$	5.03590	−	8.72243i	0.251481	−	0.435577i	0.963934	+	0.266142i	$0.0857491\pi$
$402$	−6.00000	−	6.00000i	−0.299253	−	0.299253i
$403$	−2.41154	+	1.39230i	−0.120127	+	0.0693556i
$404$	−30.9282			−1.53874
$405$			9.00000i			0.447214i
$406$		0			0
$407$		−	2.53590i		−	0.125700i
$408$	−8.19615	−	30.5885i	−0.405770	−	1.51435i
$409$	3.58846	−	2.07180i	0.177438	−	0.102444i	−0.408651	−	0.912691i	$-0.634000\pi$
$409$	3.58846	−	2.07180i	0.177438	−	0.102444i	0.586088	+	0.810247i	$0.300667\pi$
$410$	−3.46410	+	3.46410i	−0.171080	+	0.171080i
$411$	−17.6603	+	30.5885i	−0.871116	+	1.50882i
$412$	−11.7846	+	6.80385i	−0.580586	+	0.335202i
$413$		0			0
$414$		0			0
$415$	−13.3923	−	7.73205i	−0.657402	−	0.379551i
$416$	−2.53590	+	0.679492i	−0.124333	+	0.0333148i
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$	−0.588457	+	2.19615i	−0.0287824	+	0.107417i
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	1.16987	−	4.36603i	0.0569485	−	0.212535i
$423$		0			0
$424$	−1.46410	+	5.46410i	−0.0711031	+	0.265360i
$425$	−5.59808	−	3.23205i	−0.271547	−	0.156777i
$426$	−17.6603	+	4.73205i	−0.855642	+	0.229269i
$427$		0			0
$428$	2.39230	+	4.14359i	0.115636	+	0.200288i
$429$	−0.107695	+	0.186533i	−0.00519957	+	0.00900592i
$430$	2.00000	−	2.00000i	0.0964486	−	0.0964486i
$431$	−11.7679	+	6.79423i	−0.566842	+	0.327266i	−0.755887	−	0.654702i	$-0.772794\pi$
$431$	−11.7679	+	6.79423i	−0.566842	+	0.327266i	0.189045	+	0.981968i	$0.439461\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$		−	31.8564i		−	1.53092i	−0.643483	−	0.765461i	$-0.722511\pi$
$433$		−	31.8564i		−	1.53092i	0.643483	−	0.765461i	$-0.277489\pi$
$434$		0			0
$435$		−	13.7321i		−	0.658401i
$436$		−	4.14359i		−	0.198442i
$437$	−7.60770	+	4.39230i	−0.363925	+	0.210112i
$438$	22.3923	+	22.3923i	1.06995	+	1.06995i
$439$	−19.8564	+	34.3923i	−0.947695	+	1.64146i	−0.197430	+	0.980317i	$0.563260\pi$
$439$	−19.8564	+	34.3923i	−0.947695	+	1.64146i	−0.750264	+	0.661138i	$0.770074\pi$
$440$	−0.535898	−	0.535898i	−0.0255480	−	0.0255480i
$441$		0			0
$442$	−1.09808	−	4.09808i	−0.0522302	−	0.194926i
$443$	22.5167	+	13.0000i	1.06980	+	0.617649i	0.928126	−	0.372265i	$-0.121419\pi$
$443$	22.5167	+	13.0000i	1.06980	+	0.617649i	0.141672	+	0.989914i	$0.454752\pi$
$444$	−28.3923	−	16.3923i	−1.34744	−	0.777944i
$445$	−1.26795	−	2.19615i	−0.0601066	−	0.104108i
$446$	−18.7583	−	5.02628i	−0.888233	−	0.238001i
$447$	5.32051			0.251651
$448$		0			0
$449$	11.9282			0.562927			0.281463	−	0.959572i	$-0.409180\pi$
$449$	11.9282			0.562927			0.281463	+	0.959572i	$0.409180\pi$
$450$		0			0
$451$	−0.464102	−	0.803848i	−0.0218537	−	0.0378517i
$452$	9.46410	+	5.46410i	0.445154	+	0.257010i
$453$	−22.7942	−	13.1603i	−1.07097	−	0.618323i
$454$	−7.56218	−	28.2224i	−0.354911	−	1.32454i
$455$		0			0
$456$	20.7846	+	20.7846i	0.973329	+	0.973329i
$457$	−10.2679	+	17.7846i	−0.480314	+	0.831929i	−0.999745	−	0.0225837i	$-0.992811\pi$
$457$	−10.2679	+	17.7846i	−0.480314	+	0.831929i	0.519431	+	0.854513i	$0.326144\pi$
$458$	−8.53590	−	8.53590i	−0.398856	−	0.398856i
$459$	29.0885	−	16.7942i	1.35773	−	0.783887i
$460$		−	2.92820i		−	0.136528i
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$		0			0
$463$		−	16.3923i		−	0.761815i	−0.924613	−	0.380908i	$-0.875612\pi$
$463$		−	16.3923i		−	0.761815i	0.924613	−	0.380908i	$-0.124388\pi$
$464$	15.8564	+	27.4641i	0.736115	+	1.27499i
$465$	−9.00000	+	5.19615i	−0.417365	+	0.240966i
$466$	−9.07180	+	9.07180i	−0.420243	+	0.420243i
$467$	11.2583	−	19.5000i	0.520973	−	0.902352i	−0.478729	−	0.877963i	$-0.658902\pi$
$467$	11.2583	−	19.5000i	0.520973	−	0.902352i	0.999703	−	0.0243897i	$-0.00776426\pi$
$468$		0			0
$469$		0			0
$470$	−2.36603	+	0.633975i	−0.109137	+	0.0292431i
$471$	−11.7846	−	6.80385i	−0.543006	−	0.313505i
$472$	−2.53590	+	9.46410i	−0.116724	+	0.435621i
$473$	0.267949	+	0.464102i	0.0123203	+	0.0213394i
$474$	9.29423	−	34.6865i	0.426898	−	1.59321i
$475$	6.00000			0.275299
$476$		0			0
$477$		0			0
$478$	−8.77757	+	32.7583i	−0.401477	+	1.49833i
$479$	12.5885	+	21.8038i	0.575181	+	0.996243i	0.996022	+	0.0891086i	$0.0284018\pi$
$479$	12.5885	+	21.8038i	0.575181	+	0.996243i	−0.420841	+	0.907135i	$0.638265\pi$
$480$	−9.46410	+	2.53590i	−0.431975	+	0.115747i
$481$	−3.80385	−	2.19615i	−0.173441	−	0.100136i
$482$	−22.3923	+	6.00000i	−1.01994	+	0.273293i
$483$		0			0
$484$	−18.9282	+	10.9282i	−0.860373	+	0.496737i
$485$	6.69615	−	11.5981i	0.304057	−	0.526642i
$486$		0			0
$487$	−11.0718	+	6.39230i	−0.501711	+	0.289663i	−0.729420	−	0.684066i	$-0.760210\pi$
$487$	−11.0718	+	6.39230i	−0.501711	+	0.289663i	0.227709	+	0.973729i	$0.426877\pi$
$488$	6.92820	+	25.8564i	0.313625	+	1.17046i
$489$		−	36.0000i		−	1.62798i
$490$		0			0
$491$		−	9.87564i		−	0.445682i	−0.974855	−	0.222841i	$-0.928467\pi$
$491$		−	9.87564i		−	0.445682i	0.974855	−	0.222841i	$-0.0715330\pi$
$492$	−12.0000			−0.541002
$493$	−44.3827	+	25.6244i	−1.99890	+	1.15406i
$494$	2.78461	+	2.78461i	0.125286	+	0.125286i
$495$		0			0
$496$	12.0000	−	20.7846i	0.538816	−	0.933257i
$497$		0			0
$498$	−9.80385	−	36.5885i	−0.439321	−	1.63957i
$499$	−22.1603	−	12.7942i	−0.992029	−	0.572748i	−0.0861490	−	0.996282i	$-0.527456\pi$
$499$	−22.1603	−	12.7942i	−0.992029	−	0.572748i	−0.905880	+	0.423534i	$0.860789\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	−35.3205	−	9.46410i	−1.57643	−	0.422404i
$503$	15.5885			0.695055			0.347527	−	0.937670i	$-0.387021\pi$
$503$	15.5885			0.695055			0.347527	+	0.937670i	$0.387021\pi$
$504$		0			0
$505$	−15.4641			−0.688143
$506$	0.535898	+	0.143594i	0.0238236	+	0.00638351i
$507$	−11.0718	−	19.1769i	−0.491716	−	0.851677i
$508$	15.4641	−	26.7846i	0.686109	−	1.18837i
$509$	−22.3923	−	12.9282i	−0.992521	−	0.573033i	−0.0864944	−	0.996252i	$-0.527566\pi$
$509$	−22.3923	−	12.9282i	−0.992521	−	0.573033i	−0.906027	+	0.423220i	$0.860900\pi$
$510$	−4.09808	−	15.2942i	−0.181466	−	0.677240i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−15.5885	+	27.0000i	−0.688247	+	1.19208i
$514$	6.00000	+	6.00000i	0.264649	+	0.264649i
$515$	−5.89230	+	3.40192i	−0.259646	+	0.149907i
$516$	6.92820			0.304997
$517$		−	0.464102i		−	0.0204112i
$518$		0			0
$519$		−	24.8038i		−	1.08877i
$520$	−1.26795	+	0.339746i	−0.0556033	+	0.0148988i
$521$	11.7846	−	6.80385i	0.516293	−	0.298082i	−0.219124	−	0.975697i	$-0.570320\pi$
$521$	11.7846	−	6.80385i	0.516293	−	0.298082i	0.735417	+	0.677615i	$0.236986\pi$
$522$		0			0
$523$	−12.1244	+	21.0000i	−0.530161	+	0.918266i	0.469220	+	0.883081i	$0.344535\pi$
$523$	−12.1244	+	21.0000i	−0.530161	+	0.918266i	−0.999381	+	0.0351845i	$0.988798\pi$
$524$	4.39230	−	2.53590i	0.191879	−	0.110781i
$525$		0			0
$526$	15.6603	−	4.19615i	0.682820	−	0.182961i
$527$	33.5885	+	19.3923i	1.46314	+	0.844742i
$528$		−	1.85641i		−	0.0807897i
$529$	−10.4282	−	18.0622i	−0.453400	−	0.785312i
$530$	−0.732051	+	2.73205i	−0.0317983	+	0.118673i
$531$		0			0
$532$		0			0
$533$	−1.60770			−0.0696370
$534$	1.60770	−	6.00000i	0.0695718	−	0.259645i
$535$	1.19615	+	2.07180i	0.0517142	+	0.0895716i
$536$	9.46410	+	2.53590i	0.408787	+	0.109534i
$537$	9.58846	+	5.53590i	0.413772	+	0.238892i
$538$	16.3923	−	4.39230i	0.706722	−	0.189366i
$539$		0			0
$540$	−5.19615	−	9.00000i	−0.223607	−	0.387298i
$541$	−3.89230	+	6.74167i	−0.167343	+	0.289847i	−0.937485	−	0.348026i	$-0.886852\pi$
$541$	−3.89230	+	6.74167i	−0.167343	+	0.289847i	0.770142	+	0.637873i	$0.220185\pi$
$542$	−9.46410	+	9.46410i	−0.406518	+	0.406518i
$543$	−1.39230	+	0.803848i	−0.0597495	+	0.0344964i
$544$	25.8564	+	25.8564i	1.10858	+	1.10858i
$545$		−	2.07180i		−	0.0887460i
$546$		0			0
$547$			21.4641i			0.917739i	0.888504	+	0.458869i	$0.151745\pi$
$547$			21.4641i			0.917739i	−0.888504	+	0.458869i	$0.848255\pi$
$548$		−	40.7846i		−	1.74223i
$549$		0			0
$550$	−0.267949	−	0.267949i	−0.0114254	−	0.0114254i
$551$	23.7846	−	41.1962i	1.01326	−	1.75502i
$552$	5.07180	−	5.07180i	0.215870	−	0.215870i
$553$		0			0
$554$	6.14359	+	22.9282i	0.261016	+	0.974126i
$555$	−14.1962	−	8.19615i	−0.602593	−	0.347907i
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$	10.9282	+	18.9282i	0.463043	+	0.802014i	0.999111	−	0.0421611i	$-0.0134243\pi$
$557$	10.9282	+	18.9282i	0.463043	+	0.802014i	−0.536068	+	0.844175i	$0.680091\pi$
$558$		0			0
$559$	0.928203			0.0392588
$560$		0			0
$561$	3.00000			0.126660
$562$	10.8301	+	2.90192i	0.456841	+	0.122410i
$563$	9.58846	+	16.6077i	0.404105	+	0.699931i	0.994217	−	0.107391i	$-0.0342496\pi$
$563$	9.58846	+	16.6077i	0.404105	+	0.699931i	−0.590112	+	0.807322i	$0.700916\pi$
$564$	−5.19615	−	3.00000i	−0.218797	−	0.126323i
$565$	4.73205	+	2.73205i	0.199079	+	0.114938i
$566$	−4.43782	−	16.5622i	−0.186536	−	0.696160i
$567$		0			0
$568$	14.9282	−	14.9282i	0.626373	−	0.626373i
$569$	−3.53590	+	6.12436i	−0.148233	+	0.256746i	−0.930574	−	0.366103i	$-0.880692\pi$
$569$	−3.53590	+	6.12436i	−0.148233	+	0.256746i	0.782342	+	0.622849i	$0.214025\pi$
$570$	10.3923	+	10.3923i	0.435286	+	0.435286i
$571$	−5.78461	+	3.33975i	−0.242078	+	0.139764i	−0.616132	−	0.787643i	$-0.711301\pi$
$571$	−5.78461	+	3.33975i	−0.242078	+	0.139764i	0.374053	+	0.927407i	$0.377968\pi$
$572$		−	0.248711i		−	0.0103991i
$573$			12.4641i			0.520695i
$574$		0			0
$575$		−	1.46410i		−	0.0610573i
$576$		0			0
$577$	16.7942	−	9.69615i	0.699153	−	0.403656i	−0.107879	−	0.994164i	$-0.534406\pi$
$577$	16.7942	−	9.69615i	0.699153	−	0.403656i	0.807032	+	0.590508i	$0.201073\pi$
$578$	−24.7846	+	24.7846i	−1.03090	+	1.03090i
$579$	8.19615	−	14.1962i	0.340620	−	0.589972i
$580$	7.92820	+	13.7321i	0.329201	+	0.570192i
$581$		0			0
$582$	31.6865	−	8.49038i	1.31345	−	0.351938i
$583$	−0.464102	−	0.267949i	−0.0192211	−	0.0110973i
$584$	−35.3205	−	9.46410i	−1.46157	−	0.391627i
$585$		0			0
$586$	7.43782	−	27.7583i	0.307254	−	1.14669i
$587$	20.5359			0.847607			0.423804	−	0.905754i	$-0.360695\pi$
$587$	20.5359			0.847607			0.423804	+	0.905754i	$0.360695\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$	−1.26795	+	4.73205i	−0.0522006	+	0.194815i
$591$	11.5359	+	19.9808i	0.474523	+	0.821899i
$592$	37.8564			1.55589
$593$	−26.3827	−	15.2321i	−1.08341	−	0.625505i	−0.151594	−	0.988443i	$-0.548440\pi$
$593$	−26.3827	−	15.2321i	−1.08341	−	0.625505i	−0.931813	+	0.362938i	$0.881774\pi$
$594$	1.90192	−	0.509619i	0.0780369	−	0.0209099i
$595$		0			0
$596$	−5.32051	+	3.07180i	−0.217937	+	0.125826i
$597$	3.00000	−	5.19615i	0.122782	−	0.212664i
$598$	0.679492	−	0.679492i	0.0277865	−	0.0277865i
$599$	−8.76795	+	5.06218i	−0.358249	+	0.206835i	−0.668312	−	0.743881i	$-0.732983\pi$
$599$	−8.76795	+	5.06218i	−0.358249	+	0.206835i	0.310064	+	0.950716i	$0.399650\pi$
$600$	−4.73205	+	1.26795i	−0.193185	+	0.0517638i
$601$		−	14.7846i		−	0.603077i	−0.953454	−	0.301538i	$-0.902500\pi$
$601$		−	14.7846i		−	0.603077i	0.953454	−	0.301538i	$-0.0975001\pi$
$602$		0			0
$603$		0			0
$604$	30.3923			1.23665
$605$	−9.46410	+	5.46410i	−0.384770	+	0.222147i
$606$	−26.7846	−	26.7846i	−1.08805	−	1.08805i
$607$	−14.5981	+	25.2846i	−0.592518	+	1.02627i	0.401374	+	0.915914i	$0.368533\pi$
$607$	−14.5981	+	25.2846i	−0.592518	+	1.02627i	−0.993892	+	0.110357i	$0.964801\pi$
$608$	−32.7846	−	8.78461i	−1.32959	−	0.356263i
$609$		0			0
$610$	3.46410	+	12.9282i	0.140257	+	0.523448i
$611$	−0.696152	−	0.401924i	−0.0281633	−	0.0162601i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	2.36603	+	0.633975i	0.0954850	+	0.0255851i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−22.9282			−0.923055			−0.461527	−	0.887126i	$-0.652698\pi$
$617$	−22.9282			−0.923055			−0.461527	+	0.887126i	$0.652698\pi$
$618$	−16.0981	−	4.31347i	−0.647560	−	0.173513i
$619$	0.339746	+	0.588457i	0.0136555	+	0.0236521i	0.872772	−	0.488127i	$-0.162320\pi$
$619$	0.339746	+	0.588457i	0.0136555	+	0.0236521i	−0.859117	+	0.511779i	$0.828987\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	6.58846	+	3.80385i	0.264386	+	0.152643i
$622$	−2.87564	−	10.7321i	−0.115303	−	0.430316i
$623$		0			0
$624$	−2.78461	−	1.60770i	−0.111474	−	0.0643593i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.5359	−	17.5359i	−0.700875	−	0.700875i
$627$	−2.41154	+	1.39230i	−0.0963077	+	0.0556033i
$628$	15.7128			0.627009
$629$			61.1769i			2.43928i
$630$		0			0
$631$			38.9090i			1.54894i	0.632610	+	0.774471i	$0.281984\pi$
$631$			38.9090i			1.54894i	−0.632610	+	0.774471i	$0.718016\pi$
$632$	10.7321	+	40.0526i	0.426898	+	1.59321i
$633$	4.79423	−	2.76795i	0.190553	−	0.110016i
$634$	−3.07180	+	3.07180i	−0.121997	+	0.121997i
$635$	7.73205	−	13.3923i	0.306837	−	0.531457i
$636$	−6.00000	+	3.46410i	−0.237915	+	0.137361i
$637$		0			0
$638$	−2.90192	+	0.777568i	−0.114888	+	0.0307842i
$639$		0			0
$640$	8.00000	−	8.00000i	0.316228	−	0.316228i
$641$	−4.46410	−	7.73205i	−0.176321	−	0.305398i	0.764296	−	0.644865i	$-0.223086\pi$
$641$	−4.46410	−	7.73205i	−0.176321	−	0.305398i	−0.940618	+	0.339468i	$0.889753\pi$
$642$	−1.51666	+	5.66025i	−0.0598578	+	0.223392i
$643$	−7.05256			−0.278126			−0.139063	−	0.990284i	$-0.544409\pi$
$643$	−7.05256			−0.278126			−0.139063	+	0.990284i	$0.544409\pi$
$644$		0			0
$645$	3.46410			0.136399
$646$	14.1962	−	52.9808i	0.558540	−	2.08450i
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	0.745622	−	0.666369i	$-0.232153\pi$
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	−0.949904	+	0.312543i	$0.898819\pi$
$648$	6.58846	−	24.5885i	0.258819	−	0.965926i
$649$	−0.803848	−	0.464102i	−0.0315538	−	0.0182176i
$650$	−0.633975	+	0.169873i	−0.0248665	+	0.00666297i
$651$		0			0
$652$	20.7846	+	36.0000i	0.813988	+	1.40987i
$653$	−8.80385	+	15.2487i	−0.344521	+	0.596728i	−0.985267	−	0.171025i	$-0.945292\pi$
$653$	−8.80385	+	15.2487i	−0.344521	+	0.596728i	0.640745	+	0.767753i	$0.278625\pi$
$654$	3.58846	−	3.58846i	0.140320	−	0.140320i
$655$	2.19615	−	1.26795i	0.0858108	−	0.0495429i
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$		0			0
$659$		−	31.1962i		−	1.21523i	−0.794232	−	0.607615i	$-0.792126\pi$
$659$		−	31.1962i		−	1.21523i	0.794232	−	0.607615i	$-0.207874\pi$
$660$		−	0.928203i		−	0.0361303i
$661$	34.3923	−	19.8564i	1.33771	−	0.772325i	0.351239	−	0.936286i	$-0.385761\pi$
$661$	34.3923	−	19.8564i	1.33771	−	0.772325i	0.986467	+	0.163961i	$0.0524272\pi$
$662$	−26.3923	−	26.3923i	−1.02577	−	1.02577i
$663$	2.59808	−	4.50000i	0.100901	−	0.174766i
$664$	30.9282	+	30.9282i	1.20025	+	1.20025i
$665$		0			0
$666$		0			0
$667$	−10.0526	−	5.80385i	−0.389237	−	0.224726i
$668$	9.00000	+	5.19615i	0.348220	+	0.201045i
$669$	−11.8923	−	20.5981i	−0.459783	−	0.796368i
$670$	4.73205	+	1.26795i	0.182815	+	0.0489852i
$671$	−2.53590			−0.0978973
$672$		0			0
$673$	−13.1769			−0.507933			−0.253966	−	0.967213i	$-0.581735\pi$
$673$	−13.1769			−0.507933			−0.253966	+	0.967213i	$0.581735\pi$
$674$		0			0
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	22.1436	+	12.7846i	0.851677	+	0.491716i
$677$	21.9904	+	12.6962i	0.845159	+	0.487953i	0.859015	−	0.511951i	$-0.171077\pi$
$677$	21.9904	+	12.6962i	0.845159	+	0.487953i	−0.0138555	+	0.999904i	$0.504410\pi$
$678$	3.46410	+	12.9282i	0.133038	+	0.496505i
$679$		0			0
$680$	12.9282	+	12.9282i	0.495774	+	0.495774i
$681$	17.8923	−	30.9904i	0.685635	−	1.18755i
$682$	1.60770	+	1.60770i	0.0615618	+	0.0615618i
$683$	6.33975	−	3.66025i	0.242584	−	0.140056i	−0.373780	−	0.927517i	$-0.621938\pi$
$683$	6.33975	−	3.66025i	0.242584	−	0.140056i	0.616364	+	0.787462i	$0.288605\pi$
$684$		0			0
$685$		−	20.3923i		−	0.779150i
$686$		0			0
$687$		−	14.7846i		−	0.564068i
$688$	−6.92820	+	4.00000i	−0.264135	+	0.152499i
$689$	−0.803848	+	0.464102i	−0.0306242	+	0.0176809i
$690$	2.53590	−	2.53590i	0.0965400	−	0.0965400i
$691$	−11.3205	+	19.6077i	−0.430652	+	0.745912i	−0.996930	−	0.0783030i	$-0.975050\pi$
$691$	−11.3205	+	19.6077i	−0.430652	+	0.745912i	0.566277	+	0.824215i	$0.308383\pi$
$692$	14.3205	+	24.8038i	0.544384	+	0.942901i
$693$		0			0
$694$	−46.7846	+	12.5359i	−1.77592	+	0.475856i
$695$	−6.00000	−	3.46410i	−0.227593	−	0.131401i
$696$	−10.0526	+	37.5167i	−0.381041	+	1.42207i
$697$	11.1962	+	19.3923i	0.424085	+	0.734536i
$698$	−1.94744	+	7.26795i	−0.0737117	+	0.275096i
$699$	−15.7128			−0.594313
$700$		0			0
$701$	−37.7846			−1.42711			−0.713553	−	0.700602i	$-0.752915\pi$
$701$	−37.7846			−1.42711			−0.713553	+	0.700602i	$0.752915\pi$
$702$	0.882686	−	3.29423i	0.0333148	−	0.124333i
$703$	−28.3923	−	49.1769i	−1.07084	−	1.85474i
$704$	1.07180	+	1.85641i	0.0403949	+	0.0699660i
$705$	−2.59808	−	1.50000i	−0.0978492	−	0.0564933i
$706$	10.0981	−	2.70577i	0.380046	−	0.101833i
$707$		0			0
$708$	−10.3923	+	6.00000i	−0.390567	+	0.225494i
$709$	−10.5000	+	18.1865i	−0.394336	+	0.683010i	−0.993016	−	0.117978i	$-0.962359\pi$
$709$	−10.5000	+	18.1865i	−0.394336	+	0.683010i	0.598680	+	0.800988i	$0.295692\pi$
$710$	7.46410	−	7.46410i	0.280123	−	0.280123i
$711$		0			0
$712$	1.85641	+	6.92820i	0.0695718	+	0.259645i
$713$			8.78461i			0.328986i
$714$		0			0
$715$		−	0.124356i		−	0.00465064i
$716$	−12.7846			−0.477783
$717$	−35.9711	+	20.7679i	−1.34337	+	0.775593i
$718$	25.3205	+	25.3205i	0.944953	+	0.944953i
$719$	19.2679	−	33.3731i	0.718573	−	1.24461i	−0.242992	−	0.970028i	$-0.578129\pi$
$719$	19.2679	−	33.3731i	0.718573	−	1.24461i	0.961565	−	0.274577i	$-0.0885378\pi$
$720$		0			0
$721$		0			0
$722$	6.22243	+	23.2224i	0.231575	+	0.864249i
$723$	−24.5885	−	14.1962i	−0.914455	−	0.527961i
$724$	0.928203	−	1.60770i	0.0344964	−	0.0597495i
$725$	3.96410	+	6.86603i	0.147223	+	0.254998i
$726$	−25.8564	−	6.92820i	−0.959621	−	0.257130i
$727$	13.6077			0.504681			0.252341	−	0.967638i	$-0.418800\pi$
$727$	13.6077			0.504681			0.252341	+	0.967638i	$0.418800\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−17.6603	−	4.73205i	−0.653635	−	0.175141i
$731$	−6.46410	−	11.1962i	−0.239083	−	0.414105i
$732$	−16.3923	+	28.3923i	−0.605877	+	1.04941i
$733$	−9.99038	−	5.76795i	−0.369003	−	0.213044i	0.304020	−	0.952666i	$-0.401671\pi$
$733$	−9.99038	−	5.76795i	−0.369003	−	0.213044i	−0.673023	+	0.739622i	$0.735004\pi$
$734$	−4.34679	−	16.2224i	−0.160443	−	0.598781i
$735$		0			0
$736$	−2.14359	+	8.00000i	−0.0790139	+	0.294884i
$737$	−0.464102	+	0.803848i	−0.0170954	+	0.0296101i
$738$		0			0
$739$	−3.69615	+	2.13397i	−0.135965	+	0.0784995i	−0.566440	−	0.824103i	$-0.691680\pi$
$739$	−3.69615	+	2.13397i	−0.135965	+	0.0784995i	0.430474	+	0.902603i	$0.358346\pi$
$740$	18.9282			0.695815
$741$			4.82309i			0.177180i
$742$		0			0
$743$			30.3923i			1.11499i	0.830182	+	0.557493i	$0.188237\pi$
$743$			30.3923i			1.11499i	−0.830182	+	0.557493i	$0.811763\pi$
$744$	28.3923	−	7.60770i	1.04091	−	0.278912i
$745$	−2.66025	+	1.53590i	−0.0974642	+	0.0562710i
$746$	−3.60770	+	3.60770i	−0.132087	+	0.132087i
$747$		0			0
$748$	−3.00000	+	1.73205i	−0.109691	+	0.0633300i
$749$		0			0
$750$	−2.36603	+	0.633975i	−0.0863950	+	0.0231495i
$751$	22.1603	+	12.7942i	0.808639	+	0.466868i	0.846483	−	0.532416i	$-0.178716\pi$
$751$	22.1603	+	12.7942i	0.808639	+	0.466868i	−0.0378439	+	0.999284i	$0.512049\pi$
$752$	6.92820			0.252646
$753$	−22.3923	−	38.7846i	−0.816021	−	1.41339i
$754$	−1.34679	+	5.02628i	−0.0490471	+	0.183046i
$755$	15.1962			0.553045
$756$		0			0
$757$	37.8564			1.37591			0.687957	−	0.725751i	$-0.258508\pi$
$757$	37.8564			1.37591			0.687957	+	0.725751i	$0.258508\pi$
$758$	2.05256	−	7.66025i	0.0745523	−	0.278233i
$759$	0.339746	+	0.588457i	0.0123320	+	0.0213596i
$760$	−16.3923	−	4.39230i	−0.594611	−	0.159326i
$761$	36.5885	+	21.1244i	1.32633	+	0.765757i	0.984730	−	0.174088i	$-0.0556977\pi$
$761$	36.5885	+	21.1244i	1.32633	+	0.765757i	0.341600	+	0.939845i	$0.389031\pi$
$762$	36.5885	−	9.80385i	1.32546	−	0.355156i
$763$		0			0
$764$	−7.19615	−	12.4641i	−0.260348	−	0.450935i
$765$		0			0
$766$	−27.4641	+	27.4641i	−0.992318	+	0.992318i
$767$	−1.39230	+	0.803848i	−0.0502732	+	0.0290253i
$768$	27.7128			1.00000
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$		0			0
$771$			10.3923i			0.374270i
$772$			18.9282i			0.681241i
$773$	−4.79423	+	2.76795i	−0.172436	+	0.0995562i	−0.583734	−	0.811945i	$-0.698409\pi$
$773$	−4.79423	+	2.76795i	−0.172436	+	0.0995562i	0.411298	+	0.911501i	$0.365076\pi$
$774$		0			0
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	−26.7846	+	26.7846i	−0.961511	+	0.961511i
$777$		0			0
$778$	−7.63397	−	28.4904i	−0.273691	−	1.02143i
$779$	−18.0000	−	10.3923i	−0.644917	−	0.372343i
$780$	−1.39230	−	0.803848i	−0.0498525	−	0.0287824i
$781$	1.00000	+	1.73205i	0.0357828	+	0.0619777i
$782$	−12.9282	−	3.46410i	−0.462312	−	0.123876i
$783$	−41.1962			−1.47223
$784$		0			0
$785$	7.85641			0.280407
$786$	6.00000	+	1.60770i	0.214013	+	0.0573446i
$787$	16.3301	+	28.2846i	0.582106	+	1.00824i	0.995229	+	0.0975623i	$0.0311045\pi$
$787$	16.3301	+	28.2846i	0.582106	+	1.00824i	−0.413123	+	0.910675i	$0.635562\pi$
$788$	−23.0718	−	13.3205i	−0.821899	−	0.474523i
$789$	17.1962	+	9.92820i	0.612199	+	0.353453i
$790$	5.36603	+	20.0263i	0.190915	+	0.712503i
$791$		0			0
$792$		0			0
$793$	−2.19615	+	3.80385i	−0.0779877	+	0.135079i
$794$	12.4641	+	12.4641i	0.442334	+	0.442334i
$795$	−3.00000	+	1.73205i	−0.106399	+	0.0614295i
$796$			6.92820i			0.245564i
$797$		−	22.1769i		−	0.785547i	−0.919635	−	0.392773i	$-0.871516\pi$
$797$		−	22.1769i		−	0.785547i	0.919635	−	0.392773i	$-0.128484\pi$
$798$		0			0
$799$			11.1962i			0.396091i
$800$	4.00000	−	4.00000i	0.141421	−	0.141421i
$801$		0			0
$802$	−10.0718	+	10.0718i	−0.355648	+	0.355648i
$803$	1.73205	−	3.00000i	0.0611227	−	0.105868i
$804$	6.00000	+	10.3923i	0.211604	+	0.366508i
$805$		0			0
$806$	3.80385	−	1.01924i	0.133985	−	0.0359011i
$807$	18.0000	+	10.3923i	0.633630	+	0.365826i
$808$	42.2487	+	11.3205i	1.48630	+	0.398254i
$809$	−3.96410	−	6.86603i	−0.139370	−	0.241397i	0.787888	−	0.615818i	$-0.211175\pi$
$809$	−3.96410	−	6.86603i	−0.139370	−	0.241397i	−0.927258	+	0.374422i	$0.877841\pi$
$810$	3.29423	−	12.2942i	0.115747	−	0.431975i
$811$	−29.0718			−1.02085			−0.510424	−	0.859923i	$-0.670512\pi$
$811$	−29.0718			−1.02085			−0.510424	+	0.859923i	$0.670512\pi$
$812$		0			0
$813$	−16.3923			−0.574903
$814$	−0.928203	+	3.46410i	−0.0325335	+	0.121417i
$815$	10.3923	+	18.0000i	0.364027	+	0.630512i
$816$			44.7846i			1.56777i
$817$	10.3923	+	6.00000i	0.363581	+	0.209913i
$818$	−5.66025	+	1.51666i	−0.197906	+	0.0530288i
$819$		0			0
$820$	6.00000	−	3.46410i	0.209529	−	0.120972i
$821$	−13.8923	+	24.0622i	−0.484845	+	0.839776i	−0.999848	−	0.0174122i	$-0.994457\pi$
$821$	−13.8923	+	24.0622i	−0.484845	+	0.839776i	0.515004	+	0.857188i	$0.327791\pi$
$822$	35.3205	−	35.3205i	1.23194	−	1.23194i
$823$	9.58846	−	5.53590i	0.334233	−	0.192969i	−0.323486	−	0.946233i	$-0.604855\pi$
$823$	9.58846	−	5.53590i	0.334233	−	0.192969i	0.657719	+	0.753264i	$0.271522\pi$
$824$	18.5885	−	4.98076i	0.647560	−	0.173513i
$825$		−	0.464102i		−	0.0161579i
$826$		0			0
$827$			14.1436i			0.491821i	0.969293	+	0.245910i	$0.0790869\pi$
$827$			14.1436i			0.491821i	−0.969293	+	0.245910i	$0.920913\pi$
$828$		0			0
$829$	0.215390	−	0.124356i	0.00748081	−	0.00431905i	−0.496255	−	0.868177i	$-0.665292\pi$
$829$	0.215390	−	0.124356i	0.00748081	−	0.00431905i	0.503736	+	0.863858i	$0.331959\pi$
$830$	15.4641	+	15.4641i	0.536767	+	0.536767i
$831$	−14.5359	+	25.1769i	−0.504245	+	0.873377i
$832$	3.71281			0.128719
$833$		0			0
$834$	−4.39230	−	16.3923i	−0.152093	−	0.567619i
$835$	4.50000	+	2.59808i	0.155729	+	0.0899101i
$836$	1.60770	−	2.78461i	0.0556033	−	0.0963077i
$837$	15.5885	+	27.0000i	0.538816	+	0.933257i
$838$	−33.1244	−	8.87564i	−1.14426	−	0.306604i
$839$	−4.39230			−0.151639			−0.0758196	−	0.997122i	$-0.524157\pi$
$839$	−4.39230			−0.151639			−0.0758196	+	0.997122i	$0.524157\pi$
$840$		0			0
$841$	33.8564			1.16746
$842$	−25.9545	−	6.95448i	−0.894451	−	0.239667i
$843$	6.86603	+	11.8923i	0.236478	+	0.409593i
$844$	−3.19615	+	5.53590i	−0.110016	+	0.190553i
$845$	11.0718	+	6.39230i	0.380881	+	0.219902i
$846$		0			0
$847$		0			0
$848$	4.00000	−	6.92820i	0.137361	−	0.237915i
$849$	10.5000	−	18.1865i	0.360359	−	0.624160i
$850$	6.46410	+	6.46410i	0.221717	+	0.221717i
$851$	−12.0000	+	6.92820i	−0.411355	+	0.237496i
$852$	25.8564			0.885826
$853$		−	2.78461i		−	0.0953432i	−0.998863	−	0.0476716i	$-0.984820\pi$
$853$		−	2.78461i		−	0.0953432i	0.998863	−	0.0476716i	$-0.0151801\pi$
$854$		0			0
$855$		0			0
$856$	−1.75129	−	6.53590i	−0.0598578	−	0.223392i
$857$	49.9808	−	28.8564i	1.70731	−	0.985716i	0.769447	−	0.638710i	$-0.220532\pi$
$857$	49.9808	−	28.8564i	1.70731	−	0.985716i	0.937863	−	0.347006i	$-0.112802\pi$
$858$	0.215390	−	0.215390i	0.00735330	−	0.00735330i
$859$	19.8564	−	34.3923i	0.677492	−	1.17345i	−0.298242	−	0.954490i	$-0.596400\pi$
$859$	19.8564	−	34.3923i	0.677492	−	1.17345i	0.975734	−	0.218960i	$-0.0702664\pi$
$860$	−3.46410	+	2.00000i	−0.118125	+	0.0681994i
$861$		0			0
$862$	18.5622	−	4.97372i	0.632230	−	0.169406i
$863$	34.5167	+	19.9282i	1.17496	+	0.678364i	0.954843	−	0.297109i	$-0.0960226\pi$
$863$	34.5167	+	19.9282i	1.17496	+	0.678364i	0.220117	+	0.975473i	$0.429356\pi$
$864$	7.60770	+	28.3923i	0.258819	+	0.965926i
$865$	7.16025	+	12.4019i	0.243456	+	0.421678i
$866$	−11.6603	+	43.5167i	−0.396232	+	1.47876i
$867$	−42.9282			−1.45792
$868$		0			0
$869$	−3.92820			−0.133255
$870$	−5.02628	+	18.7583i	−0.170407	+	0.635967i
$871$	0.803848	+	1.39230i	0.0272373	+	0.0471764i
$872$	−1.51666	+	5.66025i	−0.0513606	+	0.191680i
$873$		0			0
$874$	12.0000	−	3.21539i	0.405906	−	0.108762i
$875$		0			0
$876$	−22.3923	−	38.7846i	−0.756566	−	1.31041i
$877$	9.19615	−	15.9282i	0.310532	−	0.537857i	−0.667946	−	0.744210i	$-0.732826\pi$
$877$	9.19615	−	15.9282i	0.310532	−	0.537857i	0.978478	+	0.206353i	$0.0661595\pi$
$878$	39.7128	−	39.7128i	1.34024	−	1.34024i
$879$	30.4808	−	17.5981i	1.02809	−	0.593568i
$880$	0.535898	+	0.928203i	0.0180651	+	0.0312897i
$881$		−	29.0718i		−	0.979454i	−0.871876	−	0.489727i	$-0.837096\pi$
$881$		−	29.0718i		−	0.979454i	0.871876	−	0.489727i	$-0.162904\pi$
$882$		0			0
$883$		−	23.6077i		−	0.794462i	−0.917719	−	0.397231i	$-0.869971\pi$
$883$		−	23.6077i		−	0.794462i	0.917719	−	0.397231i	$-0.130029\pi$
$884$			6.00000i			0.201802i
$885$	−5.19615	+	3.00000i	−0.174667	+	0.100844i
$886$	−26.0000	−	26.0000i	−0.873487	−	0.873487i
$887$	−4.26795	+	7.39230i	−0.143304	+	0.248209i	−0.928739	−	0.370735i	$-0.879106\pi$
$887$	−4.26795	+	7.39230i	−0.143304	+	0.248209i	0.785435	+	0.618944i	$0.212439\pi$
$888$	32.7846	+	32.7846i	1.10018	+	1.10018i
$889$		0			0
$890$	0.928203	+	3.46410i	0.0311134	+	0.116117i
$891$	2.08846	+	1.20577i	0.0699660	+	0.0403949i
$892$	23.7846	+	13.7321i	0.796368	+	0.459783i
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$	−7.26795	−	1.94744i	−0.243077	−	0.0651322i
$895$	−6.39230			−0.213671
$896$		0			0
$897$	1.17691			0.0392960
$898$	−16.2942	−	4.36603i	−0.543745	−	0.145696i
$899$	−23.7846	−	41.1962i	−0.793261	−	1.37397i
$900$		0			0
$901$	11.1962	+	6.46410i	0.372998	+	0.215350i
$902$	0.339746	+	1.26795i	0.0113123	+	0.0422181i
$903$		0			0
$904$	−10.9282	−	10.9282i	−0.363467	−	0.363467i
$905$	0.464102	−	0.803848i	0.0154273	−	0.0267208i
$906$	26.3205	+	26.3205i	0.874440	+	0.874440i
$907$	−28.0526	+	16.1962i	−0.931470	+	0.537784i	−0.887276	−	0.461239i	$-0.847405\pi$
$907$	−28.0526	+	16.1962i	−0.931470	+	0.537784i	−0.0441938	+	0.999023i	$0.514072\pi$
$908$			41.3205i			1.37127i
$909$		0			0
$910$		0			0
$911$		−	20.2487i		−	0.670870i	−0.942063	−	0.335435i	$-0.891117\pi$
$911$		−	20.2487i		−	0.670870i	0.942063	−	0.335435i	$-0.108883\pi$
$912$	−20.7846	−	36.0000i	−0.688247	−	1.19208i
$913$	−3.58846	+	2.07180i	−0.118761	+	0.0685665i
$914$	20.5359	−	20.5359i	0.679267	−	0.679267i
$915$	−8.19615	+	14.1962i	−0.270956	+	0.469310i
$916$	8.53590	+	14.7846i	0.282034	+	0.488497i
$917$		0			0
$918$	−45.8827	+	12.2942i	−1.51435	+	0.405770i
$919$	5.55256	+	3.20577i	0.183162	+	0.105749i	0.588777	−	0.808295i	$-0.299609\pi$
$919$	5.55256	+	3.20577i	0.183162	+	0.105749i	−0.405615	+	0.914044i	$0.632943\pi$
$920$	−1.07180	+	4.00000i	−0.0353361	+	0.131876i
$921$	1.50000	+	2.59808i	0.0494267	+	0.0856095i
$922$	10.1436	−	37.8564i	0.334061	−	1.24673i
$923$	3.46410			0.114022
$924$		0			0
$925$	9.46410			0.311178
$926$	−6.00000	+	22.3923i	−0.197172	+	0.735857i
$927$		0			0
$928$	−11.6077	−	43.3205i	−0.381041	−	1.42207i
$929$	47.1962	+	27.2487i	1.54846	+	0.894001i	0.998260	+	0.0589653i	$0.0187801\pi$
$929$	47.1962	+	27.2487i	1.54846	+	0.894001i	0.550196	+	0.835036i	$0.314553\pi$
$930$	14.1962	−	3.80385i	0.465510	−	0.124733i
$931$		0			0
$932$	15.7128	−	9.07180i	0.514690	−	0.297157i
$933$	6.80385	−	11.7846i	0.222748	−	0.385811i
$934$	−22.5167	+	22.5167i	−0.736768	+	0.736768i
$935$	−1.50000	+	0.866025i	−0.0490552	+	0.0283221i
$936$		0			0
$937$		−	25.3923i		−	0.829530i	−0.909928	−	0.414765i	$-0.863864\pi$
$937$		−	25.3923i		−	0.829530i	0.909928	−	0.414765i	$-0.136136\pi$
$938$		0			0
$939$		−	30.3731i		−	0.991188i
$940$	3.46410			0.112987
$941$	33.8038	−	19.5167i	1.10197	−	0.636225i	0.165235	−	0.986254i	$-0.447162\pi$
$941$	33.8038	−	19.5167i	1.10197	−	0.636225i	0.936739	+	0.350029i	$0.113828\pi$
$942$	13.6077	+	13.6077i	0.443363	+	0.443363i
$943$	−2.53590	+	4.39230i	−0.0825802	+	0.143033i
$944$	6.92820	−	12.0000i	0.225494	−	0.390567i
$945$		0			0
$946$	−0.196152	−	0.732051i	−0.00637747	−	0.0238010i
$947$	−19.7321	−	11.3923i	−0.641205	−	0.370200i	0.143873	−	0.989596i	$-0.454044\pi$
$947$	−19.7321	−	11.3923i	−0.641205	−	0.370200i	−0.785079	+	0.619396i	$0.787378\pi$
$948$	−25.3923	+	43.9808i	−0.824704	+	1.42843i
$949$	−3.00000	−	5.19615i	−0.0973841	−	0.168674i
$950$	−8.19615	−	2.19615i	−0.265918	−	0.0712526i
$951$	−5.32051			−0.172529
$952$		0			0
$953$	21.3205			0.690639			0.345320	−	0.938485i	$-0.387771\pi$
$953$	21.3205			0.690639			0.345320	+	0.938485i	$0.387771\pi$
$954$		0			0
$955$	−3.59808	−	6.23205i	−0.116431	−	0.201664i
$956$	23.9808	−	41.5359i	0.775593	−	1.34337i
$957$	−3.18653	−	1.83975i	−0.103006	−	0.0594705i
$958$	−9.21539	−	34.3923i	−0.297736	−	1.11116i
$959$		0			0
$960$	13.8564			0.447214
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	4.39230	+	4.39230i	0.141614	+	0.141614i
$963$		0			0
$964$	32.7846			1.05592
$965$			9.46410i			0.304660i
$966$		0			0
$967$			31.1769i			1.00258i	0.865279	+	0.501291i	$0.167141\pi$
$967$			31.1769i			1.00258i	−0.865279	+	0.501291i	$0.832859\pi$
$968$	29.8564	−	8.00000i	0.959621	−	0.257130i
$969$	58.1769	−	33.5885i	1.86891	−	1.07902i
$970$	−13.3923	+	13.3923i	−0.430001	+	0.430001i
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	−0.722688	−	0.691174i	$-0.757094\pi$
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	0.959919	+	0.280279i	$0.0904271\pi$
$972$		0			0
$973$		0			0
$974$	17.4641	−	4.67949i	0.559586	−	0.149941i
$975$	−0.696152	−	0.401924i	−0.0222947	−	0.0128719i
$976$		−	37.8564i		−	1.21175i
$977$	2.12436	+	3.67949i	0.0679642	+	0.117717i	0.898005	−	0.439985i	$-0.145016\pi$
$977$	2.12436	+	3.67949i	0.0679642	+	0.117717i	−0.830041	+	0.557703i	$0.811683\pi$
$978$	−13.1769	+	49.1769i	−0.421351	+	1.57250i
$979$	−0.679492			−0.0217167
$980$		0			0
$981$		0			0
$982$	−3.61474	+	13.4904i	−0.115351	+	0.430495i
$983$	−13.7942	−	23.8923i	−0.439968	−	0.762046i	0.557719	−	0.830030i	$-0.311677\pi$
$983$	−13.7942	−	23.8923i	−0.439968	−	0.762046i	−0.997686	+	0.0679837i	$0.978343\pi$
$984$	16.3923	+	4.39230i	0.522568	+	0.140022i
$985$	−11.5359	−	6.66025i	−0.367564	−	0.212213i
$986$	70.0070	−	18.7583i	2.22948	−	0.597387i
$987$		0			0
$988$	−2.78461	−	4.82309i	−0.0885902	−	0.153443i
$989$	1.46410	−	2.53590i	0.0465557	−	0.0806369i
$990$		0			0
$991$	40.8564	−	23.5885i	1.29785	−	0.749312i	0.317815	−	0.948153i	$-0.397051\pi$
$991$	40.8564	−	23.5885i	1.29785	−	0.749312i	0.980032	+	0.198841i	$0.0637177\pi$
$992$	−24.0000	+	24.0000i	−0.762001	+	0.762001i
$993$		−	45.7128i		−	1.45065i
$994$		0			0
$995$			3.46410i			0.109819i
$996$			53.5692i			1.69741i
$997$	4.79423	−	2.76795i	0.151835	−	0.0876618i	−0.422158	−	0.906522i	$-0.638727\pi$
$997$	4.79423	−	2.76795i	0.151835	−	0.0876618i	0.573993	+	0.818861i	$0.305394\pi$
$998$	25.5885	+	25.5885i	0.809988	+	0.809988i
$999$	−24.5885	+	42.5885i	−0.777944	+	1.34744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.b.411.1		4
4.3	odd	2		980.2.o.c.411.2		4
7.2	even	3		140.2.g.b.111.4	yes	4
7.3	odd	6		980.2.o.c.31.1		4
7.4	even	3		980.2.o.d.31.1		4
7.5	odd	6		140.2.g.a.111.4	yes	4
7.6	odd	2		980.2.o.a.411.1		4
21.2	odd	6		1260.2.c.b.811.1		4
21.5	even	6		1260.2.c.a.811.1		4
28.3	even	6	inner	980.2.o.b.31.1		4
28.11	odd	6		980.2.o.a.31.1		4
28.19	even	6		140.2.g.b.111.3	yes	4
28.23	odd	6		140.2.g.a.111.3	✓	4
28.27	even	2		980.2.o.d.411.2		4
35.2	odd	12		700.2.c.c.699.2		4
35.9	even	6		700.2.g.g.251.1		4
35.12	even	12		700.2.c.b.699.2		4
35.19	odd	6		700.2.g.f.251.1		4
35.23	odd	12		700.2.c.f.699.3		4
35.33	even	12		700.2.c.e.699.3		4
56.5	odd	6		2240.2.k.a.1791.3		4
56.19	even	6		2240.2.k.b.1791.1		4
56.37	even	6		2240.2.k.b.1791.2		4
56.51	odd	6		2240.2.k.a.1791.4		4
84.23	even	6		1260.2.c.a.811.2		4
84.47	odd	6		1260.2.c.b.811.2		4
140.19	even	6		700.2.g.g.251.2		4
140.23	even	12		700.2.c.b.699.1		4
140.47	odd	12		700.2.c.f.699.4		4
140.79	odd	6		700.2.g.f.251.2		4
140.103	odd	12		700.2.c.c.699.1		4
140.107	even	12		700.2.c.e.699.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.3	✓	4	28.23	odd	6
140.2.g.a.111.4	yes	4	7.5	odd	6
140.2.g.b.111.3	yes	4	28.19	even	6
140.2.g.b.111.4	yes	4	7.2	even	3
700.2.c.b.699.1		4	140.23	even	12
700.2.c.b.699.2		4	35.12	even	12
700.2.c.c.699.1		4	140.103	odd	12
700.2.c.c.699.2		4	35.2	odd	12
700.2.c.e.699.3		4	35.33	even	12
700.2.c.e.699.4		4	140.107	even	12
700.2.c.f.699.3		4	35.23	odd	12
700.2.c.f.699.4		4	140.47	odd	12
700.2.g.f.251.1		4	35.19	odd	6
700.2.g.f.251.2		4	140.79	odd	6
700.2.g.g.251.1		4	35.9	even	6
700.2.g.g.251.2		4	140.19	even	6
980.2.o.a.31.1		4	28.11	odd	6
980.2.o.a.411.1		4	7.6	odd	2
980.2.o.b.31.1		4	28.3	even	6	inner
980.2.o.b.411.1		4	1.1	even	1	trivial
980.2.o.c.31.1		4	7.3	odd	6
980.2.o.c.411.2		4	4.3	odd	2
980.2.o.d.31.1		4	7.4	even	3
980.2.o.d.411.2		4	28.27	even	2
1260.2.c.a.811.1		4	21.5	even	6
1260.2.c.a.811.2		4	84.23	even	6
1260.2.c.b.811.1		4	21.2	odd	6
1260.2.c.b.811.2		4	84.47	odd	6
2240.2.k.a.1791.3		4	56.5	odd	6
2240.2.k.a.1791.4		4	56.51	odd	6
2240.2.k.b.1791.1		4	56.19	even	6
2240.2.k.b.1791.2		4	56.37	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-1.00000 - 1.00000i) q^{10} +(0.232051 - 0.133975i) q^{11} -3.46410i q^{12} -0.464102i q^{13} -1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-5.59808 + 3.23205i) q^{17} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} +(-0.366025 + 0.0980762i) q^{22} +(-1.26795 - 0.732051i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.169873 + 0.633975i) q^{26} -5.19615 q^{27} +7.92820 q^{29} +(-0.633975 + 2.36603i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-0.401924 - 0.232051i) q^{33} +(8.83013 - 2.36603i) q^{34} +(4.73205 - 8.19615i) q^{37} +(-6.00000 + 6.00000i) q^{38} +(-0.696152 + 0.401924i) q^{39} +(-0.732051 - 2.73205i) q^{40} -3.46410i q^{41} +2.00000i q^{43} +0.535898 q^{44} +(1.46410 + 1.46410i) q^{46} +(0.866025 - 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-0.366025 - 1.36603i) q^{50} +(9.69615 + 5.59808i) q^{51} +(0.464102 - 0.803848i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(7.09808 + 1.90192i) q^{54} +0.267949 q^{55} -10.3923 q^{57} +(-10.8301 - 2.90192i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(1.73205 - 3.00000i) q^{60} +(-8.19615 - 4.73205i) q^{61} +(2.19615 + 8.19615i) q^{62} +8.00000i q^{64} +(0.232051 - 0.401924i) q^{65} +(0.464102 + 0.464102i) q^{66} +(-3.00000 + 1.73205i) q^{67} -12.9282 q^{68} +2.53590i q^{69} +7.46410i q^{71} +(11.1962 - 6.46410i) q^{73} +(-9.46410 + 9.46410i) q^{74} +(0.866025 - 1.50000i) q^{75} +(10.3923 - 6.00000i) q^{76} +(1.09808 - 0.294229i) q^{78} +(-12.6962 - 7.33013i) q^{79} +4.00000i q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.26795 + 4.73205i) q^{82} -15.4641 q^{83} -6.46410 q^{85} +(0.732051 - 2.73205i) q^{86} +(-6.86603 - 11.8923i) q^{87} +(-0.732051 - 0.196152i) q^{88} +(-2.19615 - 1.26795i) q^{89} +(-1.46410 - 2.53590i) q^{92} +(-5.19615 + 9.00000i) q^{93} +(-1.73205 + 1.73205i) q^{94} +(5.19615 - 3.00000i) q^{95} +(-6.92820 + 6.92820i) q^{96} -13.3923i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} - 4 q^{10} - 6 q^{11} + 8 q^{16} - 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} - 12 q^{23} - 12 q^{24} + 2 q^{25} - 18 q^{26} + 4 q^{29} - 6 q^{30} - 12 q^{31} + 8 q^{32} - 12 q^{33} + 18 q^{34} + 12 q^{37} - 24 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{44} - 8 q^{46} + 2 q^{50} + 18 q^{51} - 12 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 26 q^{58} - 12 q^{61} - 12 q^{62} - 6 q^{65} - 12 q^{66} - 12 q^{67} - 24 q^{68} + 24 q^{73} - 24 q^{74} - 6 q^{78} - 30 q^{79} + 18 q^{81} - 12 q^{82} - 48 q^{83} - 12 q^{85} - 4 q^{86} - 24 q^{87} + 4 q^{88} + 12 q^{89} + 8 q^{92}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 - 4 * q^10 - 6 * q^11 + 8 * q^16 - 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 - 12 * q^23 - 12 * q^24 + 2 * q^25 - 18 * q^26 + 4 * q^29 - 6 * q^30 - 12 * q^31 + 8 * q^32 - 12 * q^33 + 18 * q^34 + 12 * q^37 - 24 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^44 - 8 * q^46 + 2 * q^50 + 18 * q^51 - 12 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 26 * q^58 - 12 * q^61 - 12 * q^62 - 6 * q^65 - 12 * q^66 - 12 * q^67 - 24 * q^68 + 24 * q^73 - 24 * q^74 - 6 * q^78 - 30 * q^79 + 18 * q^81 - 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 - 24 * q^87 + 4 * q^88 + 12 * q^89 + 8 * q^92

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